Fig. 1

The dynamic model of multi-span spinning beams with elastic constraints"

Table 1

Convergence of the first three frequencies of a three-span spinning beam with the S-S constraint when a=6 m"

Table 2

Comparison of the first four natural frequencies for a two-span beam under different constraint conditions when Ω=0 rad/s and a=5 m"

Table 3

Comparison of the first two whirling frequencies for a two-span spinning beam under different boundary conditions when Ω=10 rad/s and a=5 m"

Fig. 2

First three natural frequencies of the C-C three-span non-spinning beam changing with the spring stiffness values at different kinds of springs: (a) linear spring with k∈[10-1 1013] N/m and (b) torsion spring with K∈[10-1 1013] N · m/rad (color online)"

Fig. 3

First three natural frequencies of the S-S non-spinning beam changing with the linear spring where k∈[10-1 1013] N/m at (a) four-span and (b) two-span (color online)"

Table 4

The spring stiffness parameters of arbitrary boundary conditions"

Table 5

The natural frequencies of multi-span spinning beams under different boundary conditions when Ω=0 rad/s"

Fig. 4

First three mode shapes of different multi-span non-spinning beams with the S-S constraint (color online)"

Fig. 5

First three mode shapes of different multi-span non-spinning beams with the E1-E1 constraint (color online)"

Fig. 6

First three mode shapes of different multi-span non-spinning beams with the E2-E2 constraint (color online)"

Fig. 7

First three mode shapes of different multi-span non-spinning beams with the E3-E3 constraint (color online)"

Fig. 8

First three whirling frequencies of different multi-span spinning beams with the S-S constraint versus the spinning speed (color online)"

Fig. 9

First three whirling frequencies of different multi-span spinning beams with the E2-E2 constraint versus the spinning speed (color online)"

Fig. 10

Effect of the axial compressive force on the first three dimensionless whirling frequencies γ of different multi-span beams with the S-S constraint at Ω=0 rad/s (color online)"

Fig. 11

Effect of the axial compressive force on the first three dimensionless whirling frequencies γ of different multi-span spinning beams with the E2-E2 constraint at Ω=10 rad/s (color online)"